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BicNET: Efficient Biclustering of Biological Networks to Unravel Non-Trivial Modules

Part of the Lecture Notes in Computer Science book series (LNBI,volume 9289)

Abstract

The discovery of dense biclusters in biological networks received an increasing attention in recent years. However, despite the importance of understanding the cell behavior, dense biclusters can only identify modules where genes, proteins or metabolites are strongly connected. These modules are thus often associated with trivial, already known interactions or background processes not necessarily related with the studied conditions. Furthermore, despite the availability of biclustering algorithms able to discover modules with more flexible coherency, their application over large-scale biological networks is hampered by efficiency bottlenecks. In this work, we propose BicNET (Biclustering NETworks), an algorithm to discover non-trivial yet coherent modules in weighted biological networks with heightened efficiency. First, we motivate the relevance of discovering network modules given by constant, symmetric and plaid biclustering models. Second, we propose a solution to discover these flexible modules without time and memory bottlenecks by seizing high efficiency gains from the inherent structural sparsity of networks. Results from the analysis of protein and gene interaction networks support the relevance and efficiency of BicNET.

Keywords

  • Bipartite Graph
  • Biological Network
  • Weighted Graph
  • Association Rule Mining
  • Frequent Itemset Mining

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.

    Let \(\mathcal {L}\) be a finite set of items, and P an itemset \(P\subseteq \mathcal {L}\). A discrete matrix D is a set of transactions in \(\mathcal {L}\), \(\{P_1,..,P_n\}\). Let the coverage \(\varPhi _{P}\) of an itemset P be the set of transactions in D in which P occurs, \(\{P_i \in D\mid P\subseteq P_i\}\), and its support \(sup_P\) be the coverage size, \(\mid \) \(\varPhi _{P}\) \(\mid \). Given D and a minimum support \(\theta \), the frequent itemset mining task aims to compute: \(\{P \mid P \subseteq \mathcal {L}, sup_P \ge \theta \}\).

    Given D, let a matrix A be the concatenation of D elements with their column indexes. Let \(\varPsi _P\) of an itemset P in A be its indexes, and \(\varUpsilon _P\) be its original items in \(\mathcal {L}\). A set of biclusters \(\cup _k (I_k,J_k)\) can be derived from frequent itemsets \(\cup _k P_k\) by mapping \((I_k,J_k)\)=\((\varPhi _{P_k},\varPsi _{P_k})\) to compose constant biclusters with coherency across rows (\((I_k,J_k)\)=\((\varPsi _{P_k},\varPhi _{P_k})\) for column-coherency) with pattern \(\varUpsilon _P\).

  2. 2.

    Sparse prior equation with decreasing sparsity until able to retrieve a non-empty set of biclusters.

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Acknowledgments

This work was supported by FCT under the project UID/CEC/ 50021/2013 and the PhD grant SFRH/BD/75924/2011 to RH.

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Correspondence to Rui Henriques .

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Henriques, R., Madeira, S.C. (2015). BicNET: Efficient Biclustering of Biological Networks to Unravel Non-Trivial Modules. In: Pop, M., Touzet, H. (eds) Algorithms in Bioinformatics. WABI 2015. Lecture Notes in Computer Science(), vol 9289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48221-6_1

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  • DOI: https://doi.org/10.1007/978-3-662-48221-6_1

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